Question: What do the following two equations represent? $-2x-3y = -2$ $2x+3y = 0$
Answer: Putting the first equation in $y = mx + b$ form gives: $-2x-3y = -2$ $-3y = 2x-2$ $y = -\dfrac{2}{3}x + \dfrac{2}{3}$ Putting the second equation in $y = mx + b$ form gives: $2x+3y = 0$ $3y = -2x$ $y = -\dfrac{2}{3}x + 0$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.